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A113041
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Number of solutions to +-p(1)+-p(2)+-...+-p(2n-1) = 2, where p(i) is the i-th prime.
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4
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1, 0, 1, 3, 9, 27, 78, 249, 782, 2574, 8676, 29714, 102162, 356797, 1268990, 4521769, 16134137, 58061535, 210499244, 767154326, 2809323733, 10342098153, 38281849044, 142249547127, 527095215036, 1966843667482, 7368829743507, 27636276043171, 103876045792060
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OFFSET
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1,4
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COMMENTS
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+-p(1)+-p(2)+-...+-p(2n) = 2 has no solutions, since the left hand side is odd.
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LINKS
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FORMULA
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a(n) = [x^2] Product_{k=1..2*n-1} (x^prime(k) + 1/x^prime(k)). - Ilya Gutkovskiy, Jan 30 2024
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MAPLE
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A113041:=proc(n) local i, j, p, t; t:= NULL; for j to 2*n-1 by 2 do p:=1; for i to j do p:=p*(x^(-ithprime(i))+x^(ithprime(i))); od; t:=t, coeff(p, x, 2); od; t; end;
# second Maple program
sp:= proc(n) sp(n):= `if`(n=0, 0, ithprime(n)+sp(n-1)) end:
b := proc(n, i) option remember; `if`(n>sp(i), 0, `if`(i=0, 1,
b(n+ithprime(i), i-1)+ b(abs(n-ithprime(i)), i-1)))
end:
a:= n-> b(2, 2*n-1):
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MATHEMATICA
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sp[n_] := sp[n] = If[n == 0, 0, Prime[n] + sp[n-1]];
b[n_, i_] := b[n, i] = If[n > sp[i], 0, If[i == 0, 1, b[n + Prime[i], i-1] + b[Abs[n - Prime[i]], i-1]]];
a[n_] := b[2, 2n-1];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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